Classify the function as linear or quadratic and identify the quadratic, linear, and constant terms. y=(3x+4)(-2x-3)

Answer:

Slope of BD

Using B( b , c ) and D(a ,0)

Slope = 0 - c / a - b

= - c / a - b

Hope this helps you

the answer is :   c / a - b

you use B( b , c ) and D(a ,0)

Answer:

lateral area =150 square feet

Step-by-step explanation:

lateral area =(perimieter of prism base) times the height of the prism

so, the perimeter of the base is 9 ft*2 + 6 ft*2 which equals 30 ft

then you multiply the perimeter of the base by the height of the prism

so, height of prism =5 ft, so 5 ft times 30 ft =150 feet

therefor, the lateral area of the prism = 150 feet squared

Answer:

180

Step-by-step explanation:

to find angle :

x =180 - 150=30

y =180-80=100

z = 180-130=50

so, 30+50+100=180

Complete Question:

In P2, find the change-of-coordinates matrix from the basis B = {1 − 3t² , 2+t− 5t² , 1 + 2t} to the standard basis C = {1, t, t²}. Then, write t² as a linear combination of the polynomials in B.

Answer:

The change of coordinate matrix is :

[tex]M = \left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right][/tex]

U = t² = 3 [1 − 3t²] - 2 [2+t− 5t²] + [1 + 2t]

Step-by-step explanation:

Let U =  {D, E, F} be any vector with respect to Basis B

U = D [1 − 3t²] + E [2+t− 5t²] + F[1 + 2t]..............(*)

U = [D+2E+F]+ t[E+2F] + t²[-3D-5E]...................(**)

In Matrix form;

[tex]\left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right] \left[\begin{array}{ccc}D\\E\\F\end{array}\right] = \left[\begin{array}{ccc}D+2E+F\\E+2F\\-3D-5E\end{array}\right][/tex]

The change of coordinate matrix is therefore,

[tex]M = \left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right][/tex]

To find D, E, F in (**) such that U = t²

D + 2E + F = 0.................(1)

E + 2F = 0.........................(2)

-3D -5E = 1........................(3)

Substituting eqn (2) into eqn (1 )

D=3F...................................(4)

Substituting equations (2) and (4) into eqn (3)

-9F+10F=1

F = 1

Put the value of F into equations (2) and (4)

E = -2(1) = -2

D = 3(1) = 3

Substituting the values of D, E, and F into (*)

U = t² = 3 [1 − 3t²] - 2 [2+t− 5t²] + [1 + 2t]

Answer:

x = 25; both labeled angles are 65º

Step-by-step explanation:

To find the value of x, recall that the angles formed by two parallel lines on the same line are equal if they correspond to each other.

In the figure given above, we have two parallel line given. The angle formed by each parallel line is corresponding to the other. Therefore, both angles formed are equal.

Thus,

(3x - 10)° = (x + 40)°

Solve for x

3x - 10 = x + 40

Subtract x from both sides

3x - 10 - x = x + 40 - x

3x - x - 10 = x - x + 40

2x - 10 = 40

Add 10 to both sides

2x - 10 + 10 = 40 + 10

2x = 50

Divide both sides by 2

2x/2 = 50/2

x = 25

*Plug in the value of x to find the measure of each labelled angles:

(3x - 10)° = 3(25) - 10 = 75 - 10 = 65°

(x + 40)° = 25 + 40 = 65°

Answer:

Step-by-step explanation:

hello

[tex]f(x)=(x-3)^2+5=x^2-6x+9+5=x^2-6x+14[/tex]

hope this helps

Answer:

The first step would be to add 22 to both sides to the equation.

Answer:

x=4

Step-by-step explanation:

5x - 20 = 0

Add 20 to each side

5x = 20

Divide by 5

5x/5 = 20/5

x =4

The zero is when x = 4

Answer:

a) 4

Step-by-step explanation:

To find the zero of 5x - 20 = 0, find the value of x.

5x - 20 = 0

Add 20 to both sides.

5x - 20 + 20 = 0 + 20

5x = 20

Divide both sides by 5.

(5x)/5 = 20/5

x = 4

The zero of 5x - 20 = 0 is 4.

Answer:

Probability is 1

Step-by-step explanation:

We are given;

mean;μ = $2,075

Standard deviation;σ = $300

n = 55

x' = $1,985

Now, we want to find x' to be at least $1,985 which is P(x' > $1,985).

The z-value is calculated from;

z = (x' - μ)/(√σ/n)

Plugging in the relevant values;

z = (1985 - 2075)/(√300/55)

z = -38.536

So, P(x' > $1,985) = P(z > -38.536)

This transforms to;

P(z < 38.536)

Probability from z distribution table is 1

Answer:

C. 35

55 degrees + 35 degrees= 90 degrees

Answer:

[tex]y =log_e(x+3)[/tex]

Step-by-step explanation:

It is given that the graph corresponds to a natural logarithmic function.

That means, the function [tex]y[/tex] has a natural log (Log with base [tex]e[/tex]) of some terms of x.

It is given that asymptote of given curve is at [tex]x= -3[/tex]. i.e. when we put value

[tex]x= -3[/tex], the function will have a value [tex]y \rightarrow \infty[/tex].

We know that natural log of 0 is not defined.

So, we can say the following:

[tex]log_e(x+a)[/tex] is not defined at [tex]x= -3[/tex]

[tex]\Rightarrow x+a =0\\\Rightarrow x = -a[/tex]

i.e. [tex]x =-a[/tex] is the point where [tex]y \rightarrow \infty[/tex]

a = 3

Hence, the function becomes:

[tex]y =log_e(x+3)[/tex]

Also, given that the graph crosses x axis at x = -2

When we put x = -2 in the function:

[tex]y =log_e(-2+3) = log_e(1) = 0[/tex]

And y axis at 1.

Put x = 0, we should get y = 1

[tex]y =log_e(0+3) = log_e(3) \approx 1[/tex]

So, the function is: [tex]y =log_e(x+3)[/tex]

Answer:

1.96 planes

Step-by-step explanation:

The computation of the number of planes is shown below:

As we know that

System Inventory  is

= Flow rate in the system × Throughput time

where,

Flow rate is

= Frequency of taken off

= 16 planes ÷ hour

= 16 ÷ 60 Planes per minute

Throughput time  is

=  runway waiting time + runway Run time

= 33 seconds +  6 minutes × 60 seconds + 48 seconds

= 441  seconds

= 441  per 60 seconds

Therefore the number of planes is

[tex]= \frac{441}{60} \times \frac{16}{60}[/tex]

= 1.96 planes

Answer:

let the number of calories from lunch be called L. As such, breakfast is then L + 128, and dinner is 2L - 400. We can then sum the three meals and equate it to the total caloric intake, the known value of 1932.

  So: 1932 = L + L + 128 + 2L - 400 = 4L - 272.

  Lunch = 551

Breakfast = 551 + 128 = 679

Dinner = 2*551 - 400 = 702

Answer:

C) 1.8 is a statistic and represents an estimate of the unknown value of a parameter of  interest.

Step-by-step explanation:

The complete question is: In a survey of sleeping habits, 8400 national adults were selected randomly and contacted by telephone.

Respondents were asked: “Typically, how many times per week do you sleep less than 6 hours during  the night?” On average, those surveyed reported an average of 1.8 nights per week in which they got  less than 6 hours of sleep. Which of the following is true with respect to this scenario?

A) 8400 is the size of the population being studied.

B) 1.8 is a parameter and represents an estimate of the unknown value of a statistic of  interest.

C) 1.8 is a statistic and represents an estimate of the unknown value of a parameter of  interest.

D) None of the above

We are given that in a survey of sleeping habits, 8400 national adults were selected randomly and contacted by telephone.  

On average, those surveyed reported an average of 1.8 nights per week in which they got  less than 6 hours of sleep.

In the question 8400 is the sample size (n) as it is taken from the population to conduct a survey.

So, the statement is not true that 8400 is the size of the population being studied. It is the size of the sample being tested.

Also, the sample mean = 1.8 nights per week, it is sample or statistic value because it is calculated using sample size value and it is an estimate or representation of the population unknown parameter.

So, the correct statement is that 1.8 is a statistic and represents an estimate of the unknown value of a parameter of  interest.

Answer:

[tex]2x + 3y[/tex]

Step-by-step explanation:

Given

Shape: Triangle

[tex]P = 5x + 2y[/tex]

Sides: [tex]2x - 3y[/tex] and [tex]x + 2y[/tex]

Required

The measure of the third side

The perimeter of a triangle is the sum of all three sides;

Let the third side be represented by Side3

Hence;

[tex]Side3 + 2x - 3y + x + 2y = 5x + 2y[/tex]

Collect like terms

[tex]Side3 + 2x + x - 3y + 2y = 5x + 2y[/tex]

[tex]Side3 + 3x - y = 5x + 2y[/tex]

Collect like terms

[tex]Side3 = 5x + 2y - 3x + y[/tex]

[tex]Side3 = 5x - 3x + 2y + y[/tex]

[tex]Side3 = 2x + 3y[/tex]

Hence, the measure of the third side is 2x + 3y

Answer:

x = 12

Step-by-step explanation:

(whole secant) x (external part) = (tangent)^2

x * 3 = 6^2

3x = 36

Divide by 3

3x/3 = 36/3

x = 12

Answer:

x = 12

Step-by-step explanation:

Apply the Secant-Tangent theorem.

The product of the length of the secant segment and its external part equals the square of the length of the tangent segment.

(whole secant) × (external part) = (tangent)²

(x) × (3) = (6)²

3x = 6²

3x = 36

(3x)/3 = 36/3

x = 12

Answer:

C

Step-by-step explanation:

Answer:

CORRECT (SELECTED)

The distribution has an outlier.

Step-by-step explanation:

An outlier is a data point far away from the rest of the data. There is a lone data point in the 000 to 111 score category.

(Choice C, Incorrect)

Answer:

1.     [tex]16 = 4^2[/tex]

2.    [tex]2 = {16}^{\frac{1}{4}}[/tex]

3.    [tex]log_2 y=z[/tex]

Step-by-step explanation:

[tex]1.\ log_2 16=4[/tex]

Write in exponential form

Using the law of logarithm which says if

[tex]log_b A=x[/tex]

then

[tex]A = b^x[/tex]

By comparison;

A = 16; b = 2 and x = 4

The expression [tex]log_2 16=4[/tex] becomes

[tex]16 = 4^2[/tex]

[tex]2.\ log_{16} 2=\frac{1}{4}[/tex]

Write in exponential form

Applying the same law as used in (1) above;

A = 2; b = 16 and [tex]x = \frac{1}{4}[/tex]

The expression [tex]log_{16} 2=\frac{1}{4}[/tex] becomes

[tex]2 = {16}^{\frac{1}{4}}[/tex]

[tex]3.\ 2^z=y[/tex]

Write in logarithm form

Using the law of logarithm which says if

[tex]b^x =A[/tex]

then

[tex]log_b A=x[/tex]

By comparison;

b = 2; x = z and A = y

The expression [tex]2^z=y[/tex] becomes

[tex]log_2 y=z[/tex]

The given equations written in exponential or logarithmic form as the case is is;

1) 2⁴ = 16

2)16^(¼) = 2

3) Log_2_y = z

Usually in logarithmic exponential functions expressions;

When we have;

Log_n_Y = 2

It means that; n² = Y

Applying that same principle to our question means that;

1) log_2_16 = 4

This will now be;

2⁴ = 16

2) log_16_2 = ¼

This will now be;

16^(¼) = 2

3) For 2^(z) = y

We have;

Log_2_y = z

Read more about properties of logarithmic exponents at; https://brainly.com/question/10005276

Answer:

The last graph.

Step-by-step explanation:

The last graph is the only one that has a constant pattern that can have a rule, which is every number is multiplied by two.

Hope this helped ! good luck :)

Answer:

[tex]z=\frac{0.30 -0.32}{\sqrt{\frac{0.32(1-0.32)}{750}}}=-1.174[/tex]  

The p value for this case would be given by:

[tex]p_v =2*P(z<-1.174)=0.240[/tex]  

For this case since the p value is higher than the significance level given we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not significantly different from 0.32 or 32 %

Step-by-step explanation:

Information given

n=750 represent the random sample taken

[tex]\hat p=0.30[/tex] estimated proportion of  people who  thought the economy is getting worse

[tex]p_o=0.32[/tex] is the value that we want to verify

[tex]\alpha=0.05[/tex] represent the significance level

z would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to check if the true proportion of interest is equal to 0.32 or not.:  

Null hypothesis:[tex]p=0.32[/tex]  

Alternative hypothesis:[tex]p \neq 0.32[/tex]  

The statistic would be given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing we got:

[tex]z=\frac{0.30 -0.32}{\sqrt{\frac{0.32(1-0.32)}{750}}}=-1.174[/tex]  

The p value for this case would be given by:

[tex]p_v =2*P(z<-1.174)=0.240[/tex]  

For this case since the p value is higher than the significance level given we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not significantly different from 0.32 or 32 %

Answer:

1. The margin of error is of 66.96 square feet.

2. The 95% confidence interval estimate for the population mean using the Student's t-distribution is between 1433.04 square feet and 1566.96 square feet

Step-by-step explanation:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 22 - 1 = 21

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 21 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.08

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.08*\frac{151}{\sqrt{22}} = 66.96[/tex]

In which s is the standard deviation of the sample.

The margin of error is of 66.96 square feet.

The lower end of the interval is the sample mean subtracted by M. So it is 1500 - 66.96 = 1433.04 square feet

The upper end of the interval is the sample mean added to M. So it is 1500 + 314 = 1566.96 square feet

The 95% confidence interval estimate for the population mean using the Student's t-distribution is between 1433.04 square feet and 1566.96 square feet

You add 7 to 1/3 and that gives 22/3

Answer:

x = 9

Step-by-step explanation:

If p and q are parallel lines then the two angles are alternate interior angles and are equal

9x +8 = 15x - 46

Subtract 9x from each side

9x-9x +8 = 15x -9x - 46

8 = 6x - 46

Add 46 to each side

54 = 6x

Divide by 6

54/6 = 6x/6

9 =x

Answer:

Explanation:

This is because you have to first make the equations equal to each other. You do this because you can see that the angles are equal to each other meaning that they are the same amount of degrees. So the equation you will have is (9x + 8) = (15x - 46).

You can take off the parenthesis.

Subtract 8 from both sides.

This will lead to

Then you have to subtract 15x from both sides.

This will have a result of

When you do this you can see that there are 2 negatives. You can cancel these out. So it will look like

Finally, you have to simplify. Divide both sides by 6.

The final result is

Hope this helped

Answer:

B. The clusters are far from each other.

Step-by-step explanation:

When there is several variation in the cluster, we use the Kmeans ++ initialization, therefore the correct answer is option B

A reflection of a point over the y -axis is shown. The rule for a reflection over the y -axis is (x,y)→(−x,y) .

:D

Answer:

100%

Step-by-step explanation:

The numbers odd or greater than 1 are 1, 2, 3, 4, 5, and 6.

6 numbers out of 6.

6/6 = 1.

P(odd or greater than 1) = 100%

Answer:

100%

Step-by-step explanation:

So the original fraction is 6/6 because is is odd and 3 and 5 also 2,4,6 are all more than 1.

Answer:

WZ ≈ 16.4 cm

Step-by-step explanation:

Step 1: Find length XZ

tan40° = XZ/15

15tan40° = XZ

XZ = 12.5865

Step 2: Find WZ

sin50° = 12.5865/WZ

WZsin50° = 12.5865

WZ = 12.5865/sin50°

WZ = 16.4305

WZ ≈ 16.4 cm

Answer:

Complementary angles are angles that add up to 90°

To find the complementary angle for an angle of 70° subtract it from 90°

That's

90° - 70° = 20

Hope this helps

Answer:

20

Step-by-step explanation:

Complementary angles add to 90 degrees

70 +x = 90

Subtract 70 from each side

70+x-70 = 90-70

x = 20

The complement is 20

Answer:

33 lbs  10 ounces

Step-by-step explanation:

   13 lb 14oz

+ 30 lb 12 oz

================

32 lbs  26 oz

But we know that 16 ounces 1 1 lb

Subtract 16 ounces and add 1 lb

32 lbs  26 oz

+1 lb   - 16 ounces

==================

33 lbs  10 ounces

Answer:

Area of Rectangle A

[tex]Area = 4x^2[/tex]

Area of Rectangle B

[tex]Area = 2x^2[/tex]

Fraction

[tex]Fraction =\frac{2}{3}[/tex]

Step-by-step explanation:

From the attached, we understand that:

The dimension of rectangle A is 2x by 2x

The dimension of rectangle B is x by 2x

Area of rectangle is calculated as thus;

[tex]Area = Length * Breadth[/tex]

Area of Rectangle A

[tex]Area = 2x * 2x[/tex]

[tex]Area = 4x^2[/tex]

Area of Rectangle B

[tex]Area = x * 2x[/tex]

[tex]Area = 2x^2[/tex]

Area of Big Rectangle

The largest rectangle is formed by merging the two rectangles together;

The dimension are 3x by 2x

The Area is as follows

[tex]Area = 2x * 3x[/tex]

[tex]Area = 6x^2[/tex]

The fraction of rectangle A in relation to the largest rectangle is calculated by dividing area of rectangle A by area of the largest rectangle;

[tex]Fraction = \frac{Rectangle\ A}{Biggest}[/tex]

[tex]Fraction =\frac{4x^2}{6x^2}[/tex]

Simplify

[tex]Fraction =\frac{2x^2 * 2}{2x^2 * 3}[/tex]

[tex]Fraction =\frac{2}{3}[/tex]